User:Polygon/Collection of BB Champions

A collection of Busy Beaver Champions including Champions for BB-Adjacent functions.

Original Busy Beaver Functions

Maximum Shifts Function (S(n,m), also commonly called BB(n,m))

2 Symbols:

	Runtime	Champions
BB(1)	$1$	1RZ--- (bbch)
BB(2)	$6$	1RB1LB_1LA1RZ (bbch) 1RB0LB_1LA1RZ (bbch) 1RB1RZ_1LB1LA (bbch) 1RB1RZ_0LB1LA (bbch) 0RB1RZ_1LA1RB (bbch)
BB(3)	$21$	1RB1RZ_1LB0RC_1LC1LA (bbch)
BB(4)	$107$	1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch)
BB(5)	$47\,176\,870$	1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch)
BB(6)	$>2\uparrow \uparrow 2\uparrow \uparrow 2\uparrow \uparrow 10$	1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch)
BB(7)	$>2\uparrow ^{11}2\uparrow ^{11}3$	1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)
BB(8)
BB(9)	$>f_{\omega }(f_{9}(2))$	1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH (bbch)
BB(10)	$>f_{\omega }^{2}(25)$	1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ (bbch)
BB(11)	$>f_{\omega }^{2}(2\uparrow \uparrow 12)>f_{\omega }^{2}(f_{3}(9))$	1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE (bbch)
BB(12)	$>f_{\omega }^{4}(2\uparrow \uparrow \uparrow 4-3)>f_{\omega }^{4}(f_{4}(2))$	0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL (bbch)
BB(14)	$>f_{\omega +1}(65\,536)>g_{64}$	1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ--- (bbch)
BB(15)	$>f_{\omega +1}(f_{\omega }(10^{57}))$	0RH1LD_1RI0RC_1RB1LD_0LD1LE_1LF1RA_1RG0LE_1RB1RG_1RD1RA_0LN0RJ_1RZ0LK_0LK1LL_1RG1LM_0LL0LL_1LO1LN_0LG1LN (bbch)
BB(16)	$>f_{\omega +1}^{2}(10^{10^{57}})$
BB(18)	$>f_{\omega +2}(f_{\omega +1}^{3}(f_{\omega }^{2}(60)))$
BB(20)	$>f_{\omega +2}^{2}(21)$
BB(21)	$>f_{\omega ^{2}}^{2}(4\uparrow \uparrow 341)$
BB(40)	$>f_{\omega ^{\omega }}(75\,500)$
BB(41)	$>f_{\omega ^{\omega }}^{4}(32)$
BB(51)	$>f_{\varepsilon _{0}+1}(8)$

3 Symbols:

	Runtime	Champions
BB(1,3)	$1$	1RZ------ (bbch)
BB(2,3)	$38$	1RB2LB1RZ_2LA2RB1LB (bbch)
BB(3,3)	$\geq 119\,112\,334\,170\,342\,541>10^{17}$	0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
BB(4,3)	$>2\uparrow \uparrow \uparrow (2^{2^{32}+1}-1)$	0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD (bbch)

4 Symbols:

	Runtime	Champions
BB(1,4)	$1$	1RZ--------- (bbch)
BB(2,4)	$3\,932\,964$	1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch)
BB(3,4)	$>2\uparrow ^{15}5$	1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC (bbch)

5 Symbols:

	Runtime	Champions
BB(1,5)	$1$	1RZ------------ (bbch)
BB(2,5)	$>10^{10^{10^{3\,314\,360}}}$	1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)
BB(3,5)	$>f_{\omega }(2\uparrow ^{15}5)>f_{\omega }^{2}(15)$	1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC (bbch)

6 Symbols:

	Runtime	Champions
BB(1,6)	$1$	1RZ--------------- (bbch)
BB(2,6)	$>10\uparrow \uparrow 10\uparrow \uparrow 10^{10^{115}}$	1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch)

Maximum Score Function (Σ)

2 Symbols:

	Score	Champions
Σ(1)	$1$	1RZ--- (bbch)
Σ(2)	$4$	1RB1LB_1LA1RZ (bbch)
Σ(3)	$6$	1RB1RZ_0RC1RB_1LC1LA (bbch) 1RB1RC_1LC1RZ_1RA0LB (bbch) 1RB1LC_1LA1RB_1LB1RZ (bbch) 1RB1RA_1LC1RZ_1RA1LB (bbch) 1RB1LC_1RC1RZ_1LA0LB (bbch)
Σ(4)	$13$	1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch) 1RB0RC_1LA1RA_1RZ1RD_1LD0LB (bbch)
Σ(5)	$4098$	1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch) 1RB1RA_1LC1LB_1RA1LD_1RA1LE_1RZ0LC (bbch)
Σ(6)	$>2\uparrow \uparrow 2\uparrow \uparrow 2\uparrow \uparrow 10$	1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch)
Σ(7)	$>2\uparrow ^{11}2\uparrow ^{11}3$	1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)

3 Symbols:

	Score	Champions
Σ(1,3)	$1$	1RZ------ (bbch)
Σ(2,3)	$9$	1RB2LB1RZ_2LA2RB1LB (bbch)
Σ(3,3)	$\geq 374\,676\,383$	0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
Σ(4,3)	$>2\uparrow \uparrow \uparrow 2^{2^{32}}$	0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD (bbch)

4 Symbols:

	Score	Champions
Σ(1,4)	$1$	1RZ--------- (bbch)
Σ(2,4)	$2050$	1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch)

5 Symbols:

	Score	Champions
Σ(1,5)	$1$	1RZ------------ (bbch)
Σ(2,5)	$>10^{10^{10^{3\,314\,360}}}$	1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)

Beeping Busy Beavers

Beeping Busy Beaver (BBB)

2 Symbols:

	Steps taken	Champions
BBB(1)	$1$
BBB(2)	$6$
BBB(3)	$55$	1LB0RB_1RA0LC_1RC1RA (bbch)
BBB(4)	$\geq 32\,779\,478$
BBB(5)	$\geq 10^{14006}$

3 Symbols:

	Steps taken	Champions
BBB(1,3)
BBB(2,3)
BBB(3,3)	$\geq 10\uparrow \uparrow 6$

Beeping Booping Busy Beaver (BBBB)

There are currently no known/available Champions for this function.

Maximum Consecutive Ones Function (Num)

2 Symbols:

	Number of Ones	Champions
num(1)	$1$	1RZ--- (bbch)
num(2)	$4$	1RB1LB_1LA1LZ (bbch)
num(3)	$6$	1RB1LC_1RC1LZ_1LA0LB (bbch)
num(4)	$12$	1RB0LA_1RC1LB_1LB1RD_1RZ0RA (bbch)
num(5)	$165$	1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB (bbch) 0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC (bbch)

Maximum Space Function (BB_space)

2 Symbols:

	Cells visited	Champions
BBspace(1,2)	$2$
BBspace(2,2)	$4$
BBspace(3,2)	$7$
BBspace(4,2)	$16$

Instruction-Limited Busy Beaver

Maximum amount of steps (BBi)

	Steps	Champions
BBi(1)	$1$	0RH (bbch) 1RH--- (bbch)
BBi(2)	$3$	0RB---_1LA--- (bbch)
BBi(3)	$5$	1RB1LB_1LA--- (bbch)
BBi(4)	$16$	1RB---_0RC---_1LC0LA (bbch)
BBi(5)	$37$	1RB2LB---_2LA2RB1LB (bbch)
BBi(6)	$123$	1RB3LA1RA0LA_2LA------3RA (bbch)
BBi(7)	$3\,932\,963$	1RB2LA1RA1RA_1LB1LA3RB--- (bbch) 1RB2LA1RA_1LC1LA2RB_---1LA--- (bbch)
BBi(8)	$>6.889\times 10^{1565}$	1RB1LA------_1RC3LB1RB---_2LA2LC---0LC (bbch)

Maximum Score (Σi)

	Score	Champions
Σi(1)	$1$	1RH--- (bbch)
Σi(2)	$2$	1RB---_1LA--- (bbch)
Σi(3)	$4$	1RB1LB_1LA--- (bbch)
Σi(4)	$5$	1RB0LB---_1LA2RA--- (bbch)
Σi(5)	$9$	1RB2LB---_2LA2RB1LB (bbch)
Σi(6)	$14$	1RB3LA1RA0LA_2LA------3RA (bbch)
Σi(7)	$2050$	1RB2LA1RA1RA_1LB1LA3RB--- (bbch) 1RB2LA1RA_1LC1LA2RB_---1LA--- (bbch)
Σi(8)	$>1.355\times 10^{783}$	1RB1LA------_1RC3LB1RB---_2LA2LC---0LC (bbch)

Reversible Turing Machines

Maximum Shifts Function (BB_rev)

2 Symbols:

	Steps	Champions
BBrev(1)
BBrev(2)	$6$	0RB1RZ_1LA1RB (bbch)
BBrev(3)	$17$	0RB1RZ_0LC1RA_1RB1LC (bbch)
BBrev(4)	$48$	1RB0LD_0LC0RB_1LA1LD_1LC1RZ (bbch)
BBrev(5)	$388$	1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA (bbch)
BBrev(6)	$\geq 537\,556$	1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA (bbch)
BBrev(7)	$>10^{19}$	1RB1LD_0LC0LD_1LC1LA_0LA1RE_0RF0RE_0RG1RF_0RB1RZ (bbch)

Maximum Score Function (Σ_rev)

2 Symbols:

	Score	Champions
Σrev(1)
Σrev(2)	$\geq 2$	0RB1RZ_1LA1RB (bbch)
Σrev(3)	$\geq 4$	0RB1RZ_0LC1RA_1RB1LC (bbch)
Σrev(4)	$\geq 6$	1RB0LD_0LC0RB_1LA1LD_1LC1RZ (bbch)
Σrev(5)	$\geq 16$	1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA (bbch)
Σrev(6)	$\geq 1161$	1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA (bbch)

Blanking Busy Beaver (BLB)

There are currently no known/available Champions for this function.

Lazy Beaver

Shifts Function (LB)

	1 State	2 States	3 States	4 States	5 States	6 States
2 Symbols	$2$	$7$	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 22}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 72}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 427}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 8407}
3 Symbols	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 23}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 351}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 189\,270}
4 Symbols	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 93}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 242\,789}
5 Symbols	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 956}
6 Symbols	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 33\,851}

Period-oriented Busy Beavers

Busy Preperiodic Beaver (BBS)

2 Symbols:

	Preperiod	Champions
BBS(1,2)
BBS(2,2)
BBS(3,2)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 101}	1RB1LB_0RC0LA_1LC0LA (bbch)
BBS(4,2)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq 119\,120\,230\,102}	1RB1LC_0LA1RD_0RB0LC_1LA0RD (bbch)

3 Symbols: It seems that currently no information is available for this domain.

4 Symbols:

	Preperiod	Champions
BBS(1,4)
BBS(2,4)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq 293\,225\,660\,896}	1RB2LA0RA3LA_1LA1LB3RB1RA (bbch)

Busy Periodic Beaver (BBP)

2 Symbols:

	Period	Champions
BBP(1,2)
BBP(2,2)
BBP(3,2)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 92}	1RB0LA_0RC1LA_1LC0RB (bbch)
BBP(4,2)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq 212\,081\,736}	1RB0LA_0RC1RD_1LD0RB_1LA1RB (bbch)

3 Symbols: It seems that currently no information is available for this domain.

4 Symbols:

	Period	Champions
BBP(1,4)
BBP(2,4)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq 33\,209\,131}	1RB0RA3LB1RB_2LA0LB1RA2RB (bbch)

Busy Beaver for Lambda Calculus (BBλ)

Regular Busy Beaver for Lambda Calculus

For n = 0,1,2,3,5 BBλ(n) is undefined, while for the rest of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 20 \geq n } BBλ(n) = n.

	BBλ(n)	Champions
BBλ(21)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 22}	\(\1 1) (1 (\2))
BBλ(22)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 24}	\(\1 1) (1 (\\1))\(\1 1 1) (1 1)
BBλ(23)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 26}	\(\1 1) (1 (\\2))
BBλ(24)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 30}	\(\1 1 1) (1 (\1))
BBλ(25)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 42}	\(\1 1) (\1 (2 1))
BBλ(26)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 52}	(\1 1) (\\2 (1 2))
BBλ(27)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 44}	\\(\1 1) (\1 (2 1))
BBλ(28)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 58}	\(\1 1) (\1 (2 (\2))))
BBλ(29)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 223}	\(\1 1) (\1 (1 (2 1)))
BBλ(30)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 160}	(\1 1 1) (\\2 (1 2)) and (\1 (1 1)) (\\2 (1 2))
BBλ(31)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 267}	(\1 1) (\\2 (2 (1 2)))
BBλ(32)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 298 }	\(\1 1) (\1 (1 (2 (\2))))
BBλ(33)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1812}	\(\1 1) (\1 (1 (1 (2 1))))
BBλ(34)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 327\,686}	(\1 1 1 1) (\\2 (2 1)) and (\1 (1 1) 1) (\\2 (2 1))
BBλ(35)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5 \times 3^{3^{3}} +6 > 3.8 \times 10^{13}}	(\1 1 1) (\\2 (2 (2 1)))
BBλ(36)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5 \times 2^{2^{2^{3}}} +6 > 5.7 \times 10^{77}}	(\1 1) (\1 (1 (\\2 (2 1))))
BBλ(37)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle BB \lambda(35) +2 =5 \times 3^{3^{3}} +8 > 3.8 \times 10^{13}}	\(\1 1 1) (\\2 (2 (2 1)))
BBλ(38)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq 5 \times 2^{2^{2^{2^{2}}}} +6 > 10^{10^{4}}}	(\1 1 1 1 1) (\\2 (2 1)) and (\1 (1 1) 1 1) (\\2 (2 1))
BBλ(39)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq 5 \times 3^{3^{3^{3}}} +6 > 10^{10^{12}}}	(\1 1 1 1) (\\2 (2 (2 1)))
BBλ(40)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > (2 \uparrow\uparrow)^{15}33 > 10 \uparrow\uparrow\uparrow 16}	(\1 1 1) (\1 (\\2 (2 1)) 1)
BBλ(41)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq 5 \times 3^{3^{85}} +6 > 10^{10^{40}}}	(\1 (\1 1) 1) (\\2 (2 (2 1)))
BBλ(42)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq BB \lambda(40) + 2 > (2 \uparrow\uparrow)^{15}33 > 10 \uparrow\uparrow\uparrow 16}	\(\1 1 1) (\1 (\\2 (2 1)) 1)
BBλ(43)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow 8}	(\1 1) (\1 (\1 (\\2 (2 1)) 2))
BBλ(44)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 16}	(\1 1 1 1) (\1 (\\2 (2 1)) 1)
BBλ(45)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq BB \lambda(43) + 2 > 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow 8}	\(\1 1) (\1 (\1 (\\2 (2 1)) 2))
BBλ(46)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq BB \lambda(44) + 2 > 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 16}	\(\1 1 1 1) (\1 (\\2 (2 1)) 1)
BBλ(47)
BBλ(48)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 16}	(\1 1 1 1 1) (\1 (\\2 (2 1)) 1)
BBλ(49)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_{\omega+1}(\frac{2 \uparrow\uparrow 6}{2}) > \text{Grahams Number}}	(\1 1) (\1 (1 (\\1 2 (\\2 (2 1)))))
BBλ(1850)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > \text{Loaders Number}}	Too large for this list

Oracle Busy Beaver for Lambda Calculus (BBλ₁)

Note that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(n) = 6 + 5 \times BB \lambda(n)} .

	BBλ1(n)	Champions
BBλ1(1)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0}
BBλ1(2)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1}	1
BBλ1(3)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0}
BBλ1(4)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4}	\1
BBλ1(5)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5}	\2
BBλ1(6)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6}	\\1
BBλ1(7)	$7$	\\2
BBλ1(8)	$26$	1 (\1)
BBλ1(9)	$9$	\\2
BBλ1(10)	$36$	1 (\\1)
BBλ1(11)	$41$	1 (\\2)
BBλ1(12)	$266$	1 (1 (\1))
BBλ1(13)	$51$	1 (\\2)
BBλ1(14)	$f(36)=25\times 2^{2^{2^{3}}}+36>2.85\times 10^{78}$	1 (1 (\\1))
BBλ1(15)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(41) \geq 25 \times 3^{3^{85}}+36 > 10^{10^{40}}}	1 (1 (\\2))
BBλ1(16)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(266)}	1 (1 (1 (\1)))
BBλ1(17)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(51)}	1 (1 (\\\2))
BBλ1(18)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f^{4}(4) = f(f(266))}	1 (\1) 1 (\1)
BBλ1(19)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f^{3}(7) = f(f(41))}	1 (1 (1 (\\2)))
BBλ1(20)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f^{6}(4) = f^{4}(266)}	1 (\\1) 1 (\1)
BBλ1(21)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f^{7}(4) = f^{5}(266)}	1 (\\2) 1 (\1)
BBλ1(22)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f^{52}(4) = f^{50}(266)}	1 (1(\1)) 1(\1)
BBλ1(28)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq f^{BB \lambda(f^{3}(4))}(4)}	1 (\1) 1 (\1) 1 (\1)

Doodle Function (doodle)

doodle(1,n) = 1 and doodle(2,n) = n

2 Symbols:

	Runtime	Champions
doodle(3,2)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \geq 487}

Terminating Turmites (TT)

There are currently no known/available Champions for this function.